Simplify the following expression: $p = \dfrac{-10a^2 + 50a + 140}{a + 2} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ p =\dfrac{-10(a^2 - 5a - 14)}{a + 2} $ Then we factor the remaining polynomial: $a^2 {-5}a {-14} $ ${2} {-7} = {-5}$ ${2} \times {-7} = {-14}$ $ (a + {2}) (a {-7}) $ This gives us a factored expression: $\dfrac{-10(a + {2}) (a {-7})}{a + 2}$ We can divide the numerator and denominator by $(a - 2)$ on condition that $a \neq -2$ Therefore $p = -10(a - 7); a \neq -2$